Difference between revisions of "Team:CIEI-China/Model"

 
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<div>Modeling</div>
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<ul class="page-anchors">
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<li><a href="#a1"> MODLE--The Influence of Hypertonicity in Anaerobic Food Waste Composting</a>
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<ul>
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<li><a href="#a2">Analysis of the Problem</a>
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</li>
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<li><a href="#a3">Model Construction</a>
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</li>
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<li><a href="#a4">Model Construction</a>
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<li><a href="#a5">Simulation and Result analysis</a>
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<li><a href="#a6">Reference</a>
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<li><a href="#a7">Appendix</a>
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<div class="first-level" id="a1"  >MODLE--The Influence of on Microbes in Anaerobic Food Waste Composting</div>
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<div class="second-level" id="a2" >Analysis of the Problem</div>
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<p class="my-content" >Food waste, which comes from citizens’ daily production and consumption, includes leftovers from restaurants, canteens, and residents’ homes. It consists of rice, flour, vegetables, plant or animal oil, meat, bones, and so on, and therefore, contains high percentages of organic substances, mainly starch, protein, cellulose, and lipids. Specific Groups in food waste may vary in different regions due to their size, function, life level, and citizens’ habits; yet in China, food waste generally has a higher level of starch and lipids, with a lower level of protein and cellulose. Because of the amount of organic substances and moisture in food waste, which is considerably larger than in other solid waste, food waste is easy to decay at high temperature, produce repulsive smell, breed bacteria and pathogens, and thus lead to tremendous harms and pollution to the surrounding areas.</p>
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<p class="my-content" >Osmosis pressure plays an important role in microbes’ life. Their living environment must have a relatively equal osmosis pressure as in their cells; if the surrounding osmosis pressure goes beyond the limits or changes all of a sudden, microbes may not be able to conduct normal activities or even die. In hypertonic solution, the cells dehydrate, protoplasma contracts, and the cell plasma becomes viscous, leading to plasmolysis. In hypotonic solution, water moves in to the cell, and cells expand or even burst. In isotonic solution, microbes metabolize the best, and the cells neither contract nor expand – they keep their original form. Normal saline (0.85% NaCl solution) is one kind of isotonic solution.</p>
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<p class="my-content" >The influence of salinity on microbes mainly includes:</p>
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<div class="third-level" >Dehydration:</div>
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<p class="my-content" >Since water naturally move from lower concentration to higher concentration, if the outside environment contains excessive salt, water inside the microbes will get lost through osmosis, resulting in the change of inner biochemical environment. The microbes will unable to perform metabolic reactions and die of dehydration.</p>
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<div class="third-level" >Interference on the absorption</div>
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<p class="my-content" >Generally, cells absorb beneficial substances, a process influenced by outside solution concentration directly. Too much salinity will interfere or even halt the absorption, and repress microbes’ metabolism.</p>
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<div class="third-level" >Poisoning</div>
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<p class="my-content" >Salt may get inside of the microbes and destroy their inner biochemical reaction processes; some may react with cell membrane and change its protective/absorption  characteristics (for example, heavy metal salt).</p>
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<p class="my-content" >During our research, we discovered that high salinity influences anaerobic composting in the following aspects: 1. Active sludge: longer adjusting period, lower growing speed in logarithm growth period, longer decelerating period; 2. Stronger microbe respiration and cell lysis; 3. Lower organic biodegradable degree; 4. Lower composting efficiency.</p>
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<p class="my-content" >In the following article, we will discuss the influence of hypertonicity and high salinity on microbes in food waste anaerobic composting through dynamic models.</p>
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<div class="second-level" id="a3" >Model Construction</div>
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<div class="third-level" > Model Analysis</div>
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<p class="my-content" >Hypertonicity and high salinity  reduce the microbe survivability  in food waste disposal, and it is a negative factor in the anaerobic fermentation, which decreases the effectiveness and efficiency of the microbes.</p>
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<p class="my-content" >Anaerobic fermentation, known as anaerobic composting or biogas fermentation, refers to the process of transforming organic crop straw, livestock manure, organic waste from industrial and domestic waste water into CH<Sub>4</sub> and CO<sub>2</sub>.</p>
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<p class="my-content" >The essence of anaerobic fermentation is the transforming process of microbial metabolism and energy conversion. The microbes utilize a small part of organic matter for microorganism’s own metabolism, and the remaining part are used for biogas production.</p>
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<p class="my-content" >Anaerobic fermentation can reduce the amount of waste, achieve the purpose of reduction, decrease environmental pollution, and produce available energy to obtain green resources. The main components of biogas are CH<Sub>4</sub> and CO<sub>2</sub> and, 60% of which is CH<Sub>4</sub>, 40% is CO<sub>2</sub>, and a small amount of etc. Different fermentation substrate produces slightly different biogas. At the same time, biogas residue and slurry produced by anaerobic fermentation can also be used as fertilizer and other agricultural purposes.</p>
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<p class="my-content" >Anaerobic composting is a process involving many stages and various microbes. People's understanding of this complex reaction process has developed through the Two-Stage Theory in the 1930s to the Three Stage Theory and the Four Stage Theory. According to the differences in microbes’ biological chemical process, Two Stage Theory divided the microbes into two groups: fermentation bacteria which produce methane and bacteria which do not produce methane, and the anaerobic composting was divided into acid and methane production stages. The acid production stage is the process through which the microbes decompose the complex organic matter into fatty acid, alcohol, and so on through hydrolysis, and the stage of methane production further transforms the substance into CH<Sub>4</sub> and CO<sub>2</sub>. This theory gives a brief description of anaerobic composting, and guide the production practice of anaerobic fermentation in the last century; however, this theory did not fully reflect the essence of anaerobic composting, and there are still some questions remaining for further researches.</p>
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<p class="my-content" >With further anaerobic composting research, people have developed a deeper understanding of the relationship between microbial populations in anaerobic composting. In 1967, Bryant introduced the Three Stage Theory of anaerobic composting in 1979. The anaerobic composting process was divided into three stages: hydrolysis, acid production and methane production. At the same time, Zeikus et al. proposed the Four Stage Theory of anaerobic composting. The anaerobic composting process was divided into four stages: hydrolysis, acid production, acetic acid production and methane production. The Four Stage Theory has clearly defined the types and roles of microbes at each stage of anaerobic composting and thus received wide acceptance.</p>
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<p class="my-content" >On the one hand, the main influencing factors of anaerobic fermentation include total solids concentration, temperature, pH value and inhibition factors. In addition, the number of microorganisms plays a key role in the anaerobic fermentation; however, hypertonicity and high salinity can affect the number of microorganisms, so we, using anaerobic fermentation effect, have to analyze the osmotic pressure and high salinity effects on microorganisms. Therefore, we constructed a model to provide a detailed analysis of our idea.</p>
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<div class="second-level" id="a4" >Model Construction</div>
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<p class="my-content" >According to different composition of particulate organic matter and the hydrolysis process, hydrolysis kinetics model of particulate organic matter (POM) is divided into 3 categories: hydrolysis model based on the concentration of POM; hydrolysis model based on particle surface area of POM; hydrolysis model based on the component of POM. Therefore, we also considered the effects of hypertonicity and high salinity on microorganisms in accordance with these three models.</p>
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<div class="forth-level" >Hydrolysis Model Based on Concentration of POM</div>
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<p class="my-content" >In Contois model, substrate concentration is related to the initial substrate concentration in the anaerobic composting, saturation constant is proportional to the initial substrate concentration. The diffusion in the matrix under high concentration limits the hydrolysis reaction, namely the particle dissolution process is the rate limiting step.</p>
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<div class="my-formula-img"><img class="my-img" src="https://static.igem.org/mediawiki/2017/9/97/T--CIEI-China--Model--1.png" /><span> (2-1)</span></div>
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<p class="my-content" >In which, <i>X<sub>s</sub></i> is the concentration of dissolved organic substances, mg/L; <i>X<sub>H</sub></i> is the concentration of undissolved organic substances, mg/L. <i>k<sub>H</sub></i> is the hydrolysis constant; <i>k<sub>x</sub></i> is the saturation hydrolysis constant.</p>
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<p class="my-content" >The following formula consider influence from the hypertonicity and high salinity:</p>
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<div class="my-formula-img"><img class="my-img" src="https://static.igem.org/mediawiki/2017/0/0e/T--CIEI-China--Model--2.png" /><span>(2-2)</span></div>
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<p class="my-content" >In which, <i>p</i> is the osmosis pressure, <i>s</i> is the salt concentration, <i>α</i> is the constant of the osmosis pressure’s influence on dissolved organic substances,<i>β</i> is the constant of the salinity’s influence on dissolved organic substances.</p>
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<p class="my-content" >Contois model was firstly applied in the hydrolysis process of dissolved organic substances in aerobic activated sludge, and was developed in anaerobic fermentation process of POM. Contois model highly fits within the anaerobic fermentation of high concentrated substances.</p>
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<div class="forth-level" >Hydrolysis Model Based on Particle Surface Area of POM</div>
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<p class="my-content" >The hydrolysis of POM is the process of gradually hydrolyzing in descending order. We applied surface area of POM into the traditional first order model in the formula:</p>
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<div class="my-formula-img"><img class="my-img" src="https://static.igem.org/mediawiki/2017/0/08/T--CIEI-China--Model--3.png" /><span>  （2-3）</span></div>
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<p class="my-content" >n which, <i>k<sub>s</sub></i> is the constant of POM hydrolysis per unit are,<i>m<sup>-2</sup>·s<sup>-1</sup></i>; <i>A</i> is the surface area of POM at <i>t</i> moment,<i>m<sup>2</sup></i>; <i>φ</i> is the constant of the increase in actual surface areas of particles due to the porosity; <i>X</i> is the concentration of undissolved POM at <i>t</i> moment, mg/L.</p>
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<p class="my-content" >Uavilin et al. Introduced the hydrolysis model based on different shapes of POM in the two-stage model:</p>
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<div class="my-formula-img"><img class="my-img" src="https://static.igem.org/mediawiki/2017/f/f2/T--CIEI-China--Model--4.png" /><span>（2-4）</span></div>
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<p class="my-content" >In which, <i>r</i> is the hydrolysis rate; <i>k</i> is the hydrolysis rate constant; <i>S, S<sub>F</sub></i> are respectively the current and initial concentration of substances; when n is 0 , 1/2, 2/3 , n means respectively the plate-like particle, cylindrical particle, and spherical particle. When n is 0, the formula fits within the zero order kinetics. Hydrolysis constant is the function of the ratio of POM size and bacteria size:</p>
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<div class="my-formula-img"><img class="my-img" src="https://static.igem.org/mediawiki/2017/e/ed/T--CIEI-China--Model--5.png" /><span> Spherical) （2-5）</span></div>
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<div class="my-formula-img"><img class="my-img" src="https://static.igem.org/mediawiki/2017/a/af/T--CIEI-China--Model--6.png" /><span> (Cylindrical)                      （2-6）</span></div>
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<p class="my-content" >In which, k is the hydrolysis rate; r<sub>m</sub>is the maximum hydrolysis rate;</p>
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<p class="my-content" ><i>p<sub>x</sub>, p<sub>s</sub></i>are respectively particle and microbe size;<i>δ</i>is the hydrolysis level of microbes;<i>d</i> is the size of the current particles.</p>
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<p class="my-content" >Considering the influence of hypertonicity and high salinity, the formula can</p>
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<p class="my-content" >Be changed as follows:</p>
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<div class="my-formula-img"><img class="my-img" src=" https://static.igem.org/mediawiki/2017/b/b6/T--CIEI-China--Model--7.png" /><span>              （2-7）</span></div>
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<p class="my-content" >In which, <i>p</i> is the osmosis pressure, <i>s</i> is the salinity, <i>α</i> is the constant of osmosis pressure’s influence on dissolved organic substances,<i>β</i>  is constant of salinity’s influence on dissolved organic substances.</p>
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<div class="forth-level" >Hydrolysis Model Based on Component of POM</div>
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<p class="my-content" >Yasui.H et al. studied the changes of gas production rates between primary and secondary sludge in the anaerobic composting process. Instead of considering secondary sludge as a whole, we take it as two kinds of hydrolysis, group 1 and 2 respectively in accordance with the hydrolysis level and Contois hydrolysis model. The fitting effect is good. The primary sludge can be regarded as a mixture of 4 components with different hydrolysis characteristics. Studies have shown that the Yasui.H model has a good fitting effect on the hydrolysis process of POM, such as food waste. Although the specific hydrolysis characteristics of each component in the Yasui.H model are not clear, it is undoubtedly a new approach. The models are shown as follows:</p>
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<div class="my-formula-img"><img class="my-img" src="https://static.igem.org/mediawiki/2017/e/ef/T--CIEI-China--Model--8.png" /><span>  （2-8）</span></div>
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<p class="my-content" >In which, <i>X<sub>s1</sub>, X<sub>s2</sub></i> are respectively the concentration of dissolved organic substance in group 1 and 2,mg/L; <i>X<sub>H1</sub>, X<sub>H2</sub></i> are respectively the concentration of undissolved organic substance in group 1 and 2.</p>
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<div class="second-level" id="a5" >Simulation and Result analysis</div>
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<p class="my-content" >Next is the analysis of the influence osmosis pressure and salinity have on soluble organic substances concentration.</p>
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<div class="third-level" >The Simulation and Result Analysis of Hydrolysis Model Based on Concentration of POM</div>
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<p class="my-content" >According to formula(2-2), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.</p>
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<p class="my-content" >Chart 3-1 Evaluation of parameter (osmosis pressure)</p>
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<table>
 +
<tr>
 +
<td>Parameter </td>
 +
<td><i>k<sub>H</sub></i></td>
 +
<td><i>k<sub>x</sub></i></td>
 +
<td><i>α</i></td>
 +
<td><i>β</i></td>
 +
<td><i>s</i></td>
 +
</tr>
 +
<tr>
 +
<td>Value(Standard Unit)</td>
 +
<td>10</td>
 +
<td>14</td>
 +
<td>0.1</td>
 +
<td>0.2</td>
 +
<td>20</td>
 +
</tr>
 +
</table>
 +
<p class="my-content" >We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.</p>
 +
<img class="my-img" src=" https://static.igem.org/mediawiki/2017/7/73/T--CIEI-China--Model--fig1.png" />
 +
<p class="my-content fig-txt" >Fig. 1 The Influence of Osmosis Pressure on the Concentration of Solute</p>
 +
<p class="my-content" >From Fig.1, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.</p>
 +
<p class="my-content" >According to formula(2-2), we then analyze the influence of osmosis pressure on microbes. Here are the parameters.</p>
 +
<p class="my-content" >Chart 3-2 Evaluation of Parameter (Salinity)</p>
 +
<table>
 +
<tr>
 +
<td>Parameter </td>
 +
<td><i>k<sub>H</sub></i></td>
 +
<td><i>k<sub>x</sub></i></td>
 +
<td><i>α</i></td>
 +
<td><i>β</i></td>
 +
<td><i>p</i></td>
 +
</tr>
 +
<tr>
 +
<td>Value (Standard Unit)</td>
 +
<td>10</td>
 +
<td>14</td>
 +
<td>0.1</td>
 +
<td>0.1</td>
 +
<td>20</td>
 +
</tr>
 +
</table>
 +
<p class="my-content" >We choose different values of salinity, and see the change in the concentration of solute. The values of salinity are 5,10,15,20.</p>
 +
<img class="my-img" src=" https://static.igem.org/mediawiki/2017/9/9e/T--CIEI-China--Model--fig2.jpg" />
 +
<p class="my-content fig-txt" >Fig. 2 The Influence of Salinity on the Concentration of Solute</p>
 +
<p class="my-content" >From Fig.2, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.</p>
 +
<div class="third-level" >The Simulation and Result Analysis of Hydrolysis Model Based on Particle Surface Area</div>
 +
<p class="my-content" >According to formula(2-7), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.</p>
 +
<p class="my-content" >Chart 3-3 Evaluation of Parameters (Osmosis Pressure)</p>
 +
<table>
 +
<tr>
 +
<td>Parameter </td>
 +
<td><i>φ</i></td>
 +
<td><i>A</i></td>
 +
<td><i>K<sub>s</sub></i></td>
 +
<td><i>β</i></td>
 +
<td><i>α</i></td>
 +
<td><i>s</i></td>
 +
</tr>
 +
<tr>
 +
<td>Value (Standard Unit) </td>
 +
<td>0.5</td>
 +
<td>2</td>
 +
<td>10</td>
 +
<td>0.1</td>
 +
<td>0.1</td>
 +
<td>20</td>
 +
</tr>
 +
</table>
 +
<p class="my-content" >We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.</p>
 +
<img class="my-img" src=" https://static.igem.org/mediawiki/2017/3/39/T--CIEI-China--Model--fig3.png" />
 +
<p class="my-content fig-txt" >Fig. 3 The Influence of Osmosis Pressure on the Concentration of Solute</p>
 +
<p class="my-content" >From Fig.3, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. If the osmosis pressure is too high, the number of the microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.</p>
 +
<p class="my-content" >According to formula(2-7), we then analyze the influence of salinity on microbes. Here are the parameters.</p>
 +
<p class="my-content" >Chart 3-4 Evaluation of Parameter (Salinity)</p>
 +
<table>
 +
<tr>
 +
<td>Parameter </td>
 +
<td><i>φ</i></td>
 +
<td><i>A</i></td>
 +
<td><i>K<sub>s</sub></i></td>
 +
<td><i>β</i></td>
 +
<td><i>α</i></td>
 +
<td><i>p</i></td>
 +
</tr>
 +
<tr>
 +
<td>Value (Standard Unit) </td>
 +
<td>0.5</td>
 +
<td>2</td>
 +
<td>10</td>
 +
<td>0.1</td>
 +
<td>0.1</td>
 +
<td>20</td>
 +
</tr>
 +
</table>
 +
<p class="my-content" >We choose different values of salinity, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.</p>
 +
<img class="my-img" src=" https://static.igem.org/mediawiki/2017/5/5b/T--CIEI-China--Model--fig4.png" />
 +
<p class="my-content fig-txt" >Fig. 4 The Influence of Salinity on the Concentration of Solute</p>
 +
<p class="my-content" >From Fig.4, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.</p>
 +
<div class="third-level" >The Simulation and Result Analysis of Hydrolysis Model Based on Component of POM</div>
 +
<p class="my-content" >According to formula(2-8), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.</p>
 +
<p class="my-content" >Chart 3-5 Evaluation of Parameter (osmosis pressure)</p>
 +
<table>
 +
<tr>
 +
<td>Parameter </td>
 +
<td><i>k<sub>H1</sub></i></td>
 +
<td><i> k<sub>H2</sub></i></td>
 +
<td><i>K<sub>x1</sub></i></td>
 +
<td><i> k<sub>x2</sub></i></td>
 +
<td><i>α</i></td>
 +
<td><i>β</i></td>
 +
<td><i>s</i></td>
 +
</tr>
 +
<tr>
 +
<td>Value (Standard Unit) </td>
 +
<td>10</td>
 +
<td>8</td>
 +
<td>14</td>
 +
<td>12</td>
 +
<td>0.1</td>
 +
<td>0.1</td>
 +
<td>20</td>
 +
</tr>
 +
</table>
 +
<p class="my-content" >We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.</p>
 +
<img class="my-img" src=" https://static.igem.org/mediawiki/2017/0/06/T--CIEI-China--Model--fig5.jpg" />
 +
<p class="my-content fig-txt" >Fig 5 The Influence of Osmosis Pressure on the Concentration of Solute in Group 1</p>
 +
<img class="my-img" src=" https://static.igem.org/mediawiki/2017/3/3d/T--CIEI-China--Model--fig6.jpg" />
 +
<p class="my-content fig-txt" >Fig. 6 The Influence of Osmosis Pressure on the Concentration of Solute in Group 2</p>
 +
<p class="my-content" >From Fig 5 and 6, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes’ number in the food waste. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.</p>
 +
<p class="my-content" >According to formula(2-8), we then analyze the influence of salinity on microbes. Here are the parameters.</p>
 +
<p class="my-content" >Chart 3-6 Evaluation of Parameter (Salinity)</p>
 +
<table>
 +
<tr>
 +
<td>Parameter </td>
 +
<td><i>k<sub>H1</sub></i></td>
 +
<td><i> k<sub>H2</sub></i></td>
 +
<td><i>K<sub>x1</sub></i></td>
 +
<td><i> k<sub>x2</sub></i></td>
 +
<td><i>α</i></td>
 +
<td><i>β</i></td>
 +
<td><i>p</i></td>
 +
</tr>
 +
<tr>
 +
<td>Value (Standard Unit) </td>
 +
<td>10</td>
 +
<td>8</td>
 +
<td>14</td>
 +
<td>12</td>
 +
<td>0.1</td>
 +
<td>0.1</td>
 +
<td>20</td>
 +
</tr>
 +
</table>
 +
<p class="my-content" >We choose different values of salinity, and see the change in the concentration of solute. The values of salinity are 5,10,15,20.</p>
 +
<img class="my-img" src=" https://static.igem.org/mediawiki/2017/4/4f/T--CIEI-China--Model--fig7.jpg" />
 +
<p class="my-content fig-txt" >Fig 7. The Influence of Salinity on the Concentration of Solute in Group 1</p>
 +
<img class="my-img" src=" https://static.igem.org/mediawiki/2017/1/13/T--CIEI-China--Model--fig8.jpg" />
 +
<p class="my-content fig-txt" >Fig 8.  The Influence of Salinity on the Concentration of Solute in Group 2</p>
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<p class="my-content" >From Fig.7 and 8, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.</p>
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<div class="second-level" id="a6" >Reference</div>
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<p class="my-content" >[1]Zhao, Y,. (2012). Process on High-Solids Anaerobic Fermentation for Converting Food Waste and Excess Sludge to Biogas[D]. Jiangnan University.</p>
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<p class="my-content" >[2]Cai, L,. (2002). Garbage Assortment is Necessary to Cope with Pollution and Develop Recycling Economics[J]. Complex Utilization of Chinese Resources, 2002,2:9-13.</p>
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<p class="my-content" >[3]Li, J,. (2008). The Preliminary Study on the Interfusion Anaerobic Fermentation of Kitchen Waste and Its Dynamic Model[D], Southwest Jiaotong University.</p>
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<p class="my-content" >[4]Qu, Z, Wang, J, &Liu, T,. (2006). The Choice of Chinese Municipal Solid Waste Composting Technology[J]. Environmental Sanitation Engineering. 2006,14(3):58-60.</p>
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<p class="my-content" >[5]Sun, Y,. (2005). Research on Municipal Solid Waste Anaerobic Composting[D]. Kunming University of Science and Technology.</p>
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<p class="my-content" >[6]Xu, D, Shen, D, Feng, H,. (2011). Discussion on Characteristics and Resource Recycling Technology of Food Residue[J]. Bulletin of Science and Technology. 2011,1:130-135.</p>
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<p class="my-content" >[7]Wu, X, Wei, K, Sha, S,. (2011). Present Status and Developing Trend of Kitchen Waste Processing in China and Abroad[J]. Agriculture Equipment & Vehicle Engineering. 2011,12:49-53.</p>
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<div class="second-level" id="a7" >Appendix</div>
  
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<div style="height: 2000px;">第一场　威司敏斯特寺院
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　　内奏丧礼哀乐。英王亨利五世葬仪队上场，送葬者培福、葛罗斯特、爱克塞特、华列克、温彻斯特、司礼官等同上。
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　　培福 让天空张起黑幕，叫白天让位给黑夜！预兆时世盛衰、国家兴亡的彗星，望你们在空中挥动你们的万丈光芒的尾巴！用你们的尾巴鞭挞那些恶毒的叛逆的星辰，以惩治它们坐视先王崩殂的罪戾！我们的先王亨利五世，因威名过盛，以致不克永年！在英格兰逝去的君王当中，有谁比得上他的高贵？
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　　葛罗斯特 英格兰有史以来，他是唯一的真命之主。他的德行足以服众；他挥动起来的宝剑的光辉，使人不敢对他逼视；他张开的两臂比龙翼更为广阔；他那双神威奕奕的眸子比正午时分的骄阳更使他的敌人目眩神昏，退避不遑。我该说些什么呢？他的功业绝非言语所能罄述；他征服四方真是易如反掌。
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　　爱克塞特 我们穿着丧服志哀，我们为什么不用鲜血来表示哀悼？先王宴驾，再也不能返回人世了。我们跟随在灵柩后边，好像拴在敌人的得胜战车后面的俘虏一般，这简直是用我们的庄严行列来为死神的可耻的胜利增光。嘿，难道我们只对那些断送我们荣光的灾星诅咒一番就算完事了吗？倒是让我们认真想一想，那些狡诈的法兰西巫师们，因为畏惧先王，竟然使用妖术和符咒来夺去他的寿算，他们的这个罪该怎样惩处才好！
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　　温彻斯特 我们的先王是受到万王之王①的福佑的。法兰西人见了他，吓得战战兢兢，甚至比末日审判的时候更加害怕。先王是替天行讨，我们教会的颂祷使他的国运昌隆。
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　　葛罗斯特 说什么教会！教会在哪儿？若不是你们那班僧侣们胡乱祈祷，他还不会如此短寿哩。你们最喜欢的是孱弱的幼主，像小学生一样，能受你们的摆布。
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　　温彻斯特 葛罗斯特，不管我们喜欢的是什么，反正你是护国公，太子也好，国家也好，都在你的掌握之中。你的老婆是个骄横的女人，她把你治得服服贴贴，比上帝或是教士都更有灵验。
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　　葛罗斯特 别提教会啦，你爱的是肉体的享乐，你除了要去诅咒你的仇人以外，终年也不见你走进礼拜堂的大门。
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　　培福 得啦，停止你们的争吵，大家和和气气的吧。让我们到祭坛那边去；司礼官们，随侍我们。我们不用金银作祭礼，我们要献上我们的武器，因为先王已死，武器已经无用。后代的人们，等着过苦日子吧。婴儿们将从母亲湿淋淋的眼眶里吮吸泪水，我们的岛国将变成咸泪遍地的沼泽，男人们将死尽杀绝，只剩下妇女们为死者哀号。亨利五世我的先王呵，我恳求您在天之灵保佑这片国土太平兴旺，不要让内战发生，把天上的灾星全都击退！您的英灵是一颗灿烂的明星，您的光辉远胜过裘力斯·凯撒和任何亮晶晶的……
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　　一使者上。
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　　使者 列位大人，敬祝你们政躬安泰！我从法兰西给你们带来了损失、屠杀、挫败的悲惨消息：居恩、香槟、里姆、奥尔良、巴黎、纪莎、波亚叠全都沦陷了。
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　　培福 汉子，你在老王的灵前说的是什么话？轻声一点，要不然，这些名城沦陷的消息会使老王爷砸碎铅制的棺盖，从棺材里爬了出来。
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　　葛罗凯特 巴黎丢了吗？卢昂投降了吗？假使老王果真复活，他听到这样的噩耗，还是要撒手归天的。
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　　爱克塞特 这些城池是怎样丢掉的？他们使用了什么诡计？
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　　使者 没有什么诡计；只是因为缺少兵丁和钱粮。兵士们都在纷纷议论，说你们这里派系纷歧，在这样的决战关头还举棋不定，争吵不休：一位大巨要节省开支，宁愿把战事拖长；另一位恨不得插翅飞翔，可是又缺乏羽翼；第三位的主张是，一文不费，只靠甜言蜜语来赢得和平。醒来吧，醒来吧，英格兰的贵胄们！不要再徘徊迂缓，让新近博得的荣光黯然失色。绣在你们铠甲上的百合花纹章②已被剪去尖儿了，英格兰的国徽已被割去半幅了。
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　　爱克塞特 假如我们在丧礼中没有流泪，听到这些噩耗，也禁不住要泪如泉涌的。
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　　培福 我既身为总管法国事务的大臣，这是我义不容辞的任务。我要抛开这些不体面的丧服，穿上我的戎装，我要为保卫我们在法兰西的领土而作战。我要让法兰西人的身上多开几个像眼睛一样的伤口，好让他们血泪交流，来哀悼他们层出不穷的灾祸。
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　　又一使者上。
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　　使者乙 大人们，请读一读这些充满灾殃的信简吧。法兰西除开几个无关重要的小城镇以外，已经全面地对英国背叛了。查理太子在里姆斯已经登上法国王位；奥尔良的庶子已经依附在他的身边；安佐公爵瑞尼埃表示对他赞助；阿朗松公爵也投奔了他。
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　　爱克塞特 那太子竟然登上王位！大伙儿都投奔了他！嗳哟，面对着这样的耻辱，叫我们向哪里投奔呢？
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　　葛罗斯特 我们哪儿也不投奔，除非奔向敌人的咽喉。培福，要是你迟疑不决，就由我亲自出征。
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　　培福 葛罗斯特，你对我勇往直前的性格难道还有什么怀疑吗？我心里已在盘算如何集合大军去踏遍法兰西全境了。
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　　使者丙上。
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　　使者丙 仁慈的大人们，当你们正为老王的遗体洒泪的时候，我不免要增添列位的烦恼。我不得不把骁勇的塔尔博爵爷败于法兰西人的消息向您报告。
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　　温彻斯特 怎么！塔尔博在战事中屈服了吗？是这样的吗？
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　　使者丙 唔，他没有屈服；塔尔博爵爷是在战争中被打垮了。当时的情况请容我详细说明。在八月十号那天，这位威风凛凛的爵爷，从围攻奥尔良的阵地上撤下来，那时他手下的部队不足六千名，而包围他的敌军却有二万三千之众。他来不及将队伍列成阵势；他弄不到掩护弓箭手的木栅，只能从篱笆上拆下一些尖端的木杙草草地插在地面上，用以代替栅栏，作为防御骑兵进攻的障碍物。战斗进行了三个钟头；英勇的塔尔博以超人的气概挥动他的长矛和宝剑建立了奇功：上百的敌人在他的矛、剑下丧命，他左冲右突，所向披靡。法国人把他当作煞神下降，全部敌军望见他都吓得魄散魂飞。我方士兵受到他的鼓舞，齐声欢呼“塔尔博！塔尔博！”一下子都冲到垓心。这一天本可稳稳地打一个漂亮的胜仗，要不是福斯托夫爵士干出懦夫的勾当。按照作战的部署，福斯托夫爵士的队伍留在后面担当接应的任务，却不料他一仗未打，就怯懦地临阵脱逃。这一来就引起全军崩溃，陷入敌人的重围，遭到一场屠杀。一个名叫瓦鲁恩的无耻之徒，为了博取法国太子的欢心，从塔尔博的背后攮了他一枪；这位盖世英雄，连整个法兰西集中了精锐的兵力也不敢对他正视的，却不料就这</div>
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Latest revision as of 15:14, 1 November 2017

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MODLE--The Influence of on Microbes in Anaerobic Food Waste Composting
Analysis of the Problem

Food waste, which comes from citizens’ daily production and consumption, includes leftovers from restaurants, canteens, and residents’ homes. It consists of rice, flour, vegetables, plant or animal oil, meat, bones, and so on, and therefore, contains high percentages of organic substances, mainly starch, protein, cellulose, and lipids. Specific Groups in food waste may vary in different regions due to their size, function, life level, and citizens’ habits; yet in China, food waste generally has a higher level of starch and lipids, with a lower level of protein and cellulose. Because of the amount of organic substances and moisture in food waste, which is considerably larger than in other solid waste, food waste is easy to decay at high temperature, produce repulsive smell, breed bacteria and pathogens, and thus lead to tremendous harms and pollution to the surrounding areas.

Osmosis pressure plays an important role in microbes’ life. Their living environment must have a relatively equal osmosis pressure as in their cells; if the surrounding osmosis pressure goes beyond the limits or changes all of a sudden, microbes may not be able to conduct normal activities or even die. In hypertonic solution, the cells dehydrate, protoplasma contracts, and the cell plasma becomes viscous, leading to plasmolysis. In hypotonic solution, water moves in to the cell, and cells expand or even burst. In isotonic solution, microbes metabolize the best, and the cells neither contract nor expand – they keep their original form. Normal saline (0.85% NaCl solution) is one kind of isotonic solution.

The influence of salinity on microbes mainly includes:

Dehydration:

Since water naturally move from lower concentration to higher concentration, if the outside environment contains excessive salt, water inside the microbes will get lost through osmosis, resulting in the change of inner biochemical environment. The microbes will unable to perform metabolic reactions and die of dehydration.

Interference on the absorption

Generally, cells absorb beneficial substances, a process influenced by outside solution concentration directly. Too much salinity will interfere or even halt the absorption, and repress microbes’ metabolism.

Poisoning

Salt may get inside of the microbes and destroy their inner biochemical reaction processes; some may react with cell membrane and change its protective/absorption characteristics (for example, heavy metal salt).

During our research, we discovered that high salinity influences anaerobic composting in the following aspects: 1. Active sludge: longer adjusting period, lower growing speed in logarithm growth period, longer decelerating period; 2. Stronger microbe respiration and cell lysis; 3. Lower organic biodegradable degree; 4. Lower composting efficiency.

In the following article, we will discuss the influence of hypertonicity and high salinity on microbes in food waste anaerobic composting through dynamic models.

Model Construction
Model Analysis

Hypertonicity and high salinity reduce the microbe survivability in food waste disposal, and it is a negative factor in the anaerobic fermentation, which decreases the effectiveness and efficiency of the microbes.

Anaerobic fermentation, known as anaerobic composting or biogas fermentation, refers to the process of transforming organic crop straw, livestock manure, organic waste from industrial and domestic waste water into CH4 and CO2.

The essence of anaerobic fermentation is the transforming process of microbial metabolism and energy conversion. The microbes utilize a small part of organic matter for microorganism’s own metabolism, and the remaining part are used for biogas production.

Anaerobic fermentation can reduce the amount of waste, achieve the purpose of reduction, decrease environmental pollution, and produce available energy to obtain green resources. The main components of biogas are CH4 and CO2 and, 60% of which is CH4, 40% is CO2, and a small amount of etc. Different fermentation substrate produces slightly different biogas. At the same time, biogas residue and slurry produced by anaerobic fermentation can also be used as fertilizer and other agricultural purposes.

Anaerobic composting is a process involving many stages and various microbes. People's understanding of this complex reaction process has developed through the Two-Stage Theory in the 1930s to the Three Stage Theory and the Four Stage Theory. According to the differences in microbes’ biological chemical process, Two Stage Theory divided the microbes into two groups: fermentation bacteria which produce methane and bacteria which do not produce methane, and the anaerobic composting was divided into acid and methane production stages. The acid production stage is the process through which the microbes decompose the complex organic matter into fatty acid, alcohol, and so on through hydrolysis, and the stage of methane production further transforms the substance into CH4 and CO2. This theory gives a brief description of anaerobic composting, and guide the production practice of anaerobic fermentation in the last century; however, this theory did not fully reflect the essence of anaerobic composting, and there are still some questions remaining for further researches.

With further anaerobic composting research, people have developed a deeper understanding of the relationship between microbial populations in anaerobic composting. In 1967, Bryant introduced the Three Stage Theory of anaerobic composting in 1979. The anaerobic composting process was divided into three stages: hydrolysis, acid production and methane production. At the same time, Zeikus et al. proposed the Four Stage Theory of anaerobic composting. The anaerobic composting process was divided into four stages: hydrolysis, acid production, acetic acid production and methane production. The Four Stage Theory has clearly defined the types and roles of microbes at each stage of anaerobic composting and thus received wide acceptance.

On the one hand, the main influencing factors of anaerobic fermentation include total solids concentration, temperature, pH value and inhibition factors. In addition, the number of microorganisms plays a key role in the anaerobic fermentation; however, hypertonicity and high salinity can affect the number of microorganisms, so we, using anaerobic fermentation effect, have to analyze the osmotic pressure and high salinity effects on microorganisms. Therefore, we constructed a model to provide a detailed analysis of our idea.

Model Construction

According to different composition of particulate organic matter and the hydrolysis process, hydrolysis kinetics model of particulate organic matter (POM) is divided into 3 categories: hydrolysis model based on the concentration of POM; hydrolysis model based on particle surface area of POM; hydrolysis model based on the component of POM. Therefore, we also considered the effects of hypertonicity and high salinity on microorganisms in accordance with these three models.

Hydrolysis Model Based on Concentration of POM

In Contois model, substrate concentration is related to the initial substrate concentration in the anaerobic composting, saturation constant is proportional to the initial substrate concentration. The diffusion in the matrix under high concentration limits the hydrolysis reaction, namely the particle dissolution process is the rate limiting step.

(2-1)

In which, Xs is the concentration of dissolved organic substances, mg/L; XH is the concentration of undissolved organic substances, mg/L. kH is the hydrolysis constant; kx is the saturation hydrolysis constant.

The following formula consider influence from the hypertonicity and high salinity:

(2-2)

In which, p is the osmosis pressure, s is the salt concentration, α is the constant of the osmosis pressure’s influence on dissolved organic substances,β is the constant of the salinity’s influence on dissolved organic substances.

Contois model was firstly applied in the hydrolysis process of dissolved organic substances in aerobic activated sludge, and was developed in anaerobic fermentation process of POM. Contois model highly fits within the anaerobic fermentation of high concentrated substances.

Hydrolysis Model Based on Particle Surface Area of POM

The hydrolysis of POM is the process of gradually hydrolyzing in descending order. We applied surface area of POM into the traditional first order model in the formula:

（2-3）

n which, ks is the constant of POM hydrolysis per unit are,m-2·s-1; A is the surface area of POM at t moment,m2; φ is the constant of the increase in actual surface areas of particles due to the porosity; X is the concentration of undissolved POM at t moment, mg/L.

Uavilin et al. Introduced the hydrolysis model based on different shapes of POM in the two-stage model:

（2-4）

In which, r is the hydrolysis rate; k is the hydrolysis rate constant; S, SF are respectively the current and initial concentration of substances; when n is 0 , 1/2, 2/3 , n means respectively the plate-like particle, cylindrical particle, and spherical particle. When n is 0, the formula fits within the zero order kinetics. Hydrolysis constant is the function of the ratio of POM size and bacteria size:

Spherical) （2-5）
(Cylindrical) （2-6）

In which, k is the hydrolysis rate; rmis the maximum hydrolysis rate;

px, psare respectively particle and microbe size;δis the hydrolysis level of microbes;d is the size of the current particles.

Considering the influence of hypertonicity and high salinity, the formula can

Be changed as follows:

（2-7）

In which, p is the osmosis pressure, s is the salinity, α is the constant of osmosis pressure’s influence on dissolved organic substances,β is constant of salinity’s influence on dissolved organic substances.

Hydrolysis Model Based on Component of POM

Yasui.H et al. studied the changes of gas production rates between primary and secondary sludge in the anaerobic composting process. Instead of considering secondary sludge as a whole, we take it as two kinds of hydrolysis, group 1 and 2 respectively in accordance with the hydrolysis level and Contois hydrolysis model. The fitting effect is good. The primary sludge can be regarded as a mixture of 4 components with different hydrolysis characteristics. Studies have shown that the Yasui.H model has a good fitting effect on the hydrolysis process of POM, such as food waste. Although the specific hydrolysis characteristics of each component in the Yasui.H model are not clear, it is undoubtedly a new approach. The models are shown as follows:

（2-8）

In which, Xs1, Xs2 are respectively the concentration of dissolved organic substance in group 1 and 2,mg/L; XH1, XH2 are respectively the concentration of undissolved organic substance in group 1 and 2.

Simulation and Result analysis

Next is the analysis of the influence osmosis pressure and salinity have on soluble organic substances concentration.

The Simulation and Result Analysis of Hydrolysis Model Based on Concentration of POM

According to formula(2-2), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.

Chart 3-1 Evaluation of parameter (osmosis pressure)

Parameter kH kx α β s
Value(Standard Unit) 10 14 0.1 0.2 20

We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.

Fig. 1 The Influence of Osmosis Pressure on the Concentration of Solute

From Fig.1, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.

According to formula(2-2), we then analyze the influence of osmosis pressure on microbes. Here are the parameters.

Chart 3-2 Evaluation of Parameter (Salinity)

Parameter kH kx α β p
Value (Standard Unit) 10 14 0.1 0.1 20

We choose different values of salinity, and see the change in the concentration of solute. The values of salinity are 5,10,15,20.

Fig. 2 The Influence of Salinity on the Concentration of Solute

From Fig.2, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.

The Simulation and Result Analysis of Hydrolysis Model Based on Particle Surface Area

According to formula(2-7), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.

Chart 3-3 Evaluation of Parameters (Osmosis Pressure)

Parameter φ A Ks β α s
Value (Standard Unit) 0.5 2 10 0.1 0.1 20

We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.

Fig. 3 The Influence of Osmosis Pressure on the Concentration of Solute

From Fig.3, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. If the osmosis pressure is too high, the number of the microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.

According to formula(2-7), we then analyze the influence of salinity on microbes. Here are the parameters.

Chart 3-4 Evaluation of Parameter (Salinity)

Parameter φ A Ks β α p
Value (Standard Unit) 0.5 2 10 0.1 0.1 20

We choose different values of salinity, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.

Fig. 4 The Influence of Salinity on the Concentration of Solute

From Fig.4, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.

The Simulation and Result Analysis of Hydrolysis Model Based on Component of POM

According to formula(2-8), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.

Chart 3-5 Evaluation of Parameter (osmosis pressure)

Parameter kH1 kH2 Kx1 kx2 α β s
Value (Standard Unit) 10 8 14 12 0.1 0.1 20

We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.

Fig 5 The Influence of Osmosis Pressure on the Concentration of Solute in Group 1

Fig. 6 The Influence of Osmosis Pressure on the Concentration of Solute in Group 2

From Fig 5 and 6, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes’ number in the food waste. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.

According to formula(2-8), we then analyze the influence of salinity on microbes. Here are the parameters.

Chart 3-6 Evaluation of Parameter (Salinity)

Parameter kH1 kH2 Kx1 kx2 α β p
Value (Standard Unit) 10 8 14 12 0.1 0.1 20

We choose different values of salinity, and see the change in the concentration of solute. The values of salinity are 5,10,15,20.

Fig 7. The Influence of Salinity on the Concentration of Solute in Group 1

Fig 8. The Influence of Salinity on the Concentration of Solute in Group 2

From Fig.7 and 8, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.

Reference

[1]Zhao, Y,. (2012). Process on High-Solids Anaerobic Fermentation for Converting Food Waste and Excess Sludge to Biogas[D]. Jiangnan University.

[2]Cai, L,. (2002). Garbage Assortment is Necessary to Cope with Pollution and Develop Recycling Economics[J]. Complex Utilization of Chinese Resources, 2002,2:9-13.

[3]Li, J,. (2008). The Preliminary Study on the Interfusion Anaerobic Fermentation of Kitchen Waste and Its Dynamic Model[D], Southwest Jiaotong University.

[4]Qu, Z, Wang, J, &Liu, T,. (2006). The Choice of Chinese Municipal Solid Waste Composting Technology[J]. Environmental Sanitation Engineering. 2006,14(3):58-60.

[5]Sun, Y,. (2005). Research on Municipal Solid Waste Anaerobic Composting[D]. Kunming University of Science and Technology.

[6]Xu, D, Shen, D, Feng, H,. (2011). Discussion on Characteristics and Resource Recycling Technology of Food Residue[J]. Bulletin of Science and Technology. 2011,1:130-135.

[7]Wu, X, Wei, K, Sha, S,. (2011). Present Status and Developing Trend of Kitchen Waste Processing in China and Abroad[J]. Agriculture Equipment & Vehicle Engineering. 2011,12:49-53.

Appendix
	
clear
%Model 1
%Osmosis Pressure
k_x=14;
k_h=10;
a=0.1;
b=0.2;
s=20;
p=5;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'b')
hold on
p=10;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'r')
p=15;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'g')
p=20;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘The influence of osmosis pressure on concentration of solute’)
grid on
clear
%Salinity
figure
k_x=14;
k_h=10;
a=0.1;
b=0.1;
p=20;
s=5;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)+a*p-b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'b')
hold on
s=10;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)+a*p-b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'r')
s=15;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)+a*p-b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'g')
s=20;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)+a*p-b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'k')
xlabel('time')
ylabel('X_s')
legend('s=5','s=10','s=15','s=20')
title(‘The influence of salinity on concentration of solute’)
grid on
clear
%Model 1
%Osmosis pressure
fai=0.5;
A=2;
k_s=10;
a=0.1;
b=0.1;
s=20;
p=5;
f=@(t,x)[-fai*A*k_s*x-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'b')
hold on
p=10;
f=@(t,x)[-fai*A*k_s*x-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'r')
p=15;
f=@(t,x)[-fai*A*k_s*x-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'g')
p=20;
f=@(t,x)[-fai*A*k_s*x-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘The influence of osmosis pressure on concentration of solue’)
grid on
clear
%Salinity
figure
fai=0.5;
A=2;
k_s=10;
a=0.1;
b=0.1;
p=20;
s=5;
f=@(t,x)[-fai*A*k_s*x+a*p-b*s];
[t,y]=ode23(f,[0 10],0.6);
plot(t,y,'b')
hold on
s=10;
f=@(t,x)[-fai*A*k_s*x+a*p-b*s];
[t,y]=ode23(f,[0 10],0.6);
plot(t,y,'r')
s=15;
f=@(t,x)[-fai*A*k_s*x+a*p-b*s];
[t,y]=ode23(f,[0 10],0.6);
plot(t,y,'g')
s=20;
f=@(t,x)[-fai*A*k_s*x+a*p-b*s];
[t,y]=ode23(f,[0 10],0.6);
plot(t,y,'k')
xlabel('time')
ylabel('X_s')
legend('s=5','s=10','s=15','s=20')
title(‘The influence of salinity on concentration of solute’)
grid on
clear
%Model 1
%Osmosis pressure
k_x=14;
k_x2=12;
k_h2=8;
k_h=10;
a=0.1;
b=0.2;
s=20;
p=5;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))-a*p+b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))-a*p+b*s];
[t1,y1]=ode23(f,[0 10],[0.5,0.4]);
p=10;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))-a*p+b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))-a*p+b*s];
[t2,y2]=ode23(f,[0 10],[0.5,0.4]);
p=15;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))-a*p+b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))-a*p+b*s];

[t3,y3]=ode23(f,[0 10],[0.5,0.4]);
p=20;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))-a*p+b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))-a*p+b*s];
[t4,y4]=ode23(f,[0 10],[0.5,0.4]);
hold on
plot(t1,y1(:,1),'b')
plot(t2,y2(:,1),'r')
plot(t3,y3(:,1),'g')
plot(t4,y4(:,1),'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘ The influence of osmosis pressure of Group 1 on concentration of solute’)
grid on
figure
hold on
plot(t1,y1(:,2),'b')
plot(t2,y2(:,2),'r')
plot(t3,y3(:,2),'g')
plot(t4,y4(:,2),'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘ The influence of osmosis pressure of Group 2 on concentration of solute’)
grid on
clear
%Salinity
figure
k_x=14;
k_x2=12;
k_h2=8;
k_h=10;
a=0.1;
b=0.1;
p=20;
s=5;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))+a*p-b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))+a*p-b*s];
[t1,y1]=ode23(f,[0 10],[0.5,0.4]);
s=10;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))+a*p-b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))+a*p-b*s];
[t2,y2]=ode23(f,[0 10],[0.5,0.4]);
s=15;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))+a*p-b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))+a*p-b*s];

[t3,y3]=ode23(f,[0 10],[0.5,0.4]);
s=20;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))+a*p-b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))+a*p-b*s];
[t4,y4]=ode23(f,[0 10],[0.5,0.4]);
hold on
plot(t1,y1(:,1),'b')
plot(t2,y2(:,1),'r')
plot(t3,y3(:,1),'g')
plot(t4,y4(:,1),'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘ The influence of osmosis pressure of Group 1 on concentration of solute’)

grid on
figure
hold on
plot(t1,y1(:,2),'b')
plot(t2,y2(:,2),'r')
plot(t3,y3(:,2),'g')
plot(t4,y4(:,2),'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘ The influence of osmosis pressure of Group 2 on concentration of solute’)

grid on